Method of modeling a mask by taking into account of mask pattern edge interaction

ABSTRACT

A mask layout is received. An interaction-free mask model is applied to the mask layout. An edge interaction model is applied to the mask layout. The edge interaction model describes an influence due to a plurality of combinations of two or more edges interacting with one another. A thin mask model is applied to the mask layout. A near field is determined based on the applying of the interaction-free mask model, the applying of the edge interaction model, and the applying of the thin mask model.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 62/427,308, filed on Nov. 29, 2016, and entitled“Photolithography Mask Model Accuracy Improvement for Edge Interactionfrom Arbitrary Layouts.” the disclosure of which is hereby incorporatedherein by reference in its entirety.

BACKGROUND

The semiconductor device industry has experienced rapid growth. In thecourse of semiconductor device evolution, the functional density hasgenerally increased while feature size has decreased. This scaling downprocess generally provides benefits by increasing production efficiencyand lowering associated costs. Such scaling down has also increased thecomplexity of design and manufacturing these devices.

One technique applied to the design and manufacturing of semiconductordevices is optical proximity correction (OPC). OPC includes applyingfeatures that will alter the photomask design of the layout of thesemiconductor device in order to compensate for distortions caused bydiffraction of radiation and the chemical process of photo-resist thatoccur during the use of the lithography tools. Thus, OPC provides forproducing circuit patterns on a substrate that more closely conform to asemiconductor device designer's (e.g., integrated circuit (IC) designer)layout for the device. OPC includes all resolution enhancementtechniques performed with a reticle or photomask including, for example,adding sub-resolution features to the photomask that interact with theoriginal patterns in the physical design, adding features to theoriginal patterns such as “serifs,” adding jogs to features in theoriginal pattern, modifying main feature pattern shapes or edges, andother enhancements. As process nodes shrink, OPC processes and theresultant patterns become more complex.

One type of advanced OPC involves inverse lithography technology (ILT).ILT includes simulating the optical lithography process in the reversedirection, using the desired pattern on the substrate as an input to thesimulations. The ILT process may produce complex, curvilinear patternson a photomask or reticle, rather than the Manhattan patterns that areformed on conventional photomasks or reticles. Unfortunately,conventional ILT photomasks and the methods of fabrication thereof stillface various difficulties with respect to the non-Manhattan patterns.

Therefore, although existing ILT photomasks have been generally adequatefor their intended purposes, they have not been entirely satisfactory inall respects, in particular the missing of an accurate mask modelcapable of dealing with non-Manhattan patterns.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the present disclosure are best understood from the followingdetailed description when read with the accompanying figures. It isnoted that, in accordance with the standard practice in the industry,various features are not drawn to scale. In fact, the dimensions of thevarious features may be arbitrarily increased or reduced for clarity ofdiscussion.

FIG. 1 is a simplified block diagram of an embodiment of an integratedcircuit (IC) manufacturing system according to various aspects of thepresent disclosure.

FIG. 2 is a detailed block diagram of the mask house according tovarious aspects of the present disclosure.

FIG. 3 is a graphical illustration of how a near field of a mask isgenerated according to various aspects of the present disclosure.

FIG. 4 is a flowchart of a method illustrating a process flow accordingto various aspects of the present disclosure.

FIG. 5 is a graphical illustration of an example non-Manhattan patternand a plurality of two-dimensional kernels for that pattern according tovarious aspects of the present disclosure.

FIG. 6 is a graphical illustration of a decomposition and rotation ofthe two-dimensional kernels according to various aspects of the presentdisclosure.

FIG. 7 is a graphical illustration of how to use two-dimensional kernelsto perform an edge correction process for a non-Manhattan mask patternaccording to various aspects of the present disclosure.

FIG. 8 is a flowchart illustrating a method of preparing thetwo-dimensional kernels according to various aspects of the presentdisclosure.

FIG. 9 illustrates a simplified example of how two-dimensional kernelsare generated by a regression analysis according to various aspects ofthe present disclosure.

FIG. 10 illustrates the non-Manhattan mask pattern and an aerial imageprojected by the non-Manhattan pattern on a wafer according to variousaspects of the present disclosure.

FIG. 11 is a flowchart illustrating a method of modeling a maskaccording to various aspects of the present disclosure.

FIG. 12 is a graphical illustration of an edge interaction between twoadjacent mask patterns according to various aspects of the presentdisclosure.

FIG. 13 is a flowchart of a method illustrating a process flow accordingto various aspects of the present disclosure.

FIG. 14 is a flowchart of a method of determining edge interactionsaccording to various aspects of the present disclosure.

FIG. 15 is a graphical illustration of how a two-edge (2E) kernel worksaccording to various aspects of the present disclosure.

FIG. 16 is a graphical illustration of how a three-edge (3E) kernelworks according to various aspects of the present disclosure.

FIG. 17 illustrates two techniques for accelerating the computations ofthe edge interaction according to various aspects of the presentdisclosure.

FIG. 18 is a graphical illustration of how to use the edge interactionkernels to perform an edge interaction correction process according tovarious aspects of the present disclosure.

FIG. 19 is a flowchart illustrating a method of obtaining thetwo-dimensional edge interaction kernels according to various aspects ofthe present disclosure.

FIG. 20 illustrates some mathematical relations among the edgeinteraction, the edge interaction kernels, and the mask patternaccording to various aspects of the present disclosure.

FIG. 21 is a flowchart illustrating a method of modeling a maskaccording to various aspects of the present disclosure.

DETAILED DESCRIPTION

The following disclosure provides many different embodiments, orexamples, for implementing different features of the invention. Specificexamples of components and arrangements are described below to simplifythe present disclosure. These are, of course, merely examples and arenot intended to be limiting. For example, the formation of a firstfeature over or on a second feature in the description that follows mayinclude embodiments in which the first and second features are formed indirect contact, and may also include embodiments in which additionalfeatures may be formed between the first and second features, such thatthe first and second features may not be in direct contact. In addition,the present disclosure may repeat reference numerals and/or letters inthe various examples. This repetition is for the purpose of simplicityand clarity and does not in itself dictate a relationship between thevarious embodiments and/or configurations discussed.

Further, spatially relative terms, such as “beneath,” “below,” “lower,”“above,” “upper” and the like, may be used herein for ease ofdescription to describe one element or feature's relationship to anotherelement(s) or feature(s) as illustrated in the figures. The spatiallyrelative terms are intended to encompass different orientations of thedevice in use or operation in addition to the orientation depicted inthe figures. The apparatus may be otherwise oriented (rotated 90 degreesor at other orientations) and the spatially relative descriptors usedherein may likewise be interpreted accordingly.

As semiconductor fabrication progresses to increasingly small technologynodes, various techniques are employed to help achieve the small devicesizes. One example of such technique is inverse lithography technology(ILT). In more detail, conventional lithography masks typically useManhattan patterns for IC features, which include polygons with straightedges (e.g., rectangles, squares, etc.). In older semiconductortechnology nodes, the IC features fabricated on a wafer (using theconventional lithography masks) can reasonably approximate the Manhattanpatterns on the lithography masks. However, as device size scaling downcontinues, the geometries on the lithography mask may deviatesignificantly from the actually-fabricated IC features and theirrespective Manhattan patterns on the wafer. While the deviation mayenhance the process window of fabrication, it also creates modelingchallenges.

ILT resolves the above problem by treating optical proximity correction(OPC) as an inverse imaging problem and computes a lithography maskpattern using an entire area of a design pattern rather than just edgesof the design pattern. While ILT may in some cases produce unintuitivemask patterns (such as freeform or arbitrary-shaped patterns that do nothave straight or linear edges), ILT may be used to fabricate maskshaving high fidelity and/or substantially improved depth-of-focus andexposure latitude, thereby enabling printing of features (i.e.,geometric patterns) that may otherwise have been unattainable.

However, ILT may present other challenges as well. For example,conventional techniques of modeling lithography masks are optimized forManhattan patterns. In other words, these conventional lithography maskmodeling techniques assume the patterns on the lithography mask onlyhave straight or linear edges. Since ILT uses lithography masks withpatterns that have non-straight or curvilinear edges (e.g., patternshaving arbitrary angles), conventional mask lithography modeling doesnot work well for ILT masks.

The present disclosure overcomes the problem discussed above bygenerating two-dimensional kernels that can be rotated fast in order toaccurately model an ILT lithography mask having the freeform orarbitrary mask patterns. The various aspects of the present disclosureare discussed in more detail below with reference to FIGS. 1-21.

FIG. 1 is a simplified block diagram of an embodiment of an integratedcircuit (IC) manufacturing system 100 and an IC manufacturing flowassociated therewith, which may benefit from various aspects of thepresent disclosure. The IC manufacturing system 100 includes a pluralityof entities, such as a design house 120, a mask house 130, and an ICmanufacturer 150 (i.e., a fab), that interact with one another in thedesign, development, and manufacturing cycles and/or services related tomanufacturing an integrated circuit (IC) device 160. The plurality ofentities are connected by a communications network, which may be asingle network or a variety of different networks, such as an intranetand the Internet. and may include wired and/or wireless communicationchannels. Each entity may interact with other entities and may provideservices to and/or receive services from the other entities. One or moreof the design house 120, mask house 130, and IC manufacturer 150 mayhave a common owner, and may even coexist in a common facility and usecommon resources.

In various embodiments, the design house 120, which may include one ormore design teams, generates an IC design layout 122. The IC designlayout 122 may include various geometrical patterns designed for thefabrication of the IC device 160. By way of example, the geometricalpatterns may correspond to patterns of metal, oxide, or semiconductorlayers that make up the various components of the IC device 160 to befabricated. The various layers combine to form various features of theIC device 160. For example, various portions of the IC design layout 122may include features such as an active region, a gate electrode, sourceand drain regions, metal lines or vias of a metal interconnect, openingsfor bond pads, as well as other features known in the art which are tobe formed within a semiconductor substrate (e.g., such as a siliconwafer) and various material layers disposed on the semiconductorsubstrate. In various examples, the design house 120 implements a designprocedure to form the IC design layout 122. The design procedure mayinclude logic design, physical design, and/or place and route. The ICdesign layout 122 may be presented in one or more data files havinginformation related to the geometrical patterns which are to be used forfabrication of the IC device 160. In some examples, the IC design layout122 may be expressed in a GDSII file format or DFII file format.

In some embodiments, the design house 120 may transmit the IC designlayout 122 to the mask house 130, for example, via the networkconnection described above. The mask house 130 may then use the ICdesign layout 122 to manufacture one or more masks to be used forfabrication of the various layers of the IC device 160 according to theIC design layout 122. In various examples, the mask house 130 performsmask data preparation 132, where the IC design layout 122 is translatedinto a form that can be physically written by a mask writer, and maskfabrication 144, where the design layout prepared by the mask datapreparation 132 is modified to comply with a particular mask writerand/or mask manufacturer and is then fabricated. In the example of FIG.1, the mask data preparation 132 and mask fabrication 144 areillustrated as separate elements; however, in some embodiments, the maskdata preparation 132 and mask fabrication 144 may be collectivelyreferred to as mask data preparation.

In some examples, the mask data preparation 132 includes application ofone or more resolution enhancement technologies (RETs) to compensate forpotential lithography errors, such as those that can arise fromdiffraction, interference, or other process effects. In some examples,optical proximity correction (OPC) may be used to adjust line widthsdepending on the density of surrounding geometries, add “dog-bone”end-caps to the end of lines to prevent line end shortening, correct forelectron beam (e-beam) proximity effects, or for other purposes as knownin the art. For example, OPC techniques may add sub-resolution assistfeatures (SRAFs), which for example may include adding scattering bars,serifs, and/or hammerheads to the IC design layout 122 according tooptical models or rules such that, after a lithography process, a finalpattern on a wafer is improved with enhanced resolution and precision.The mask data preparation 132 may also include further RETs, such asoff-axis illumination (OAI), phase-shifting masks (PSM), other suitabletechniques, or combinations thereof.

One technique that may be used in conjunction with OPC is inverselithography technology (ILT), which treats OPC as an inverse imagingproblem and computes a mask pattern using an entire area of a designpattern rather than just edges of the design pattern. While ILT may insome cases produce unintuitive mask patterns, ILT may be used tofabricate masks having high fidelity and/or substantially improveddepth-of-focus and exposure latitude, thereby enabling printing offeatures (i.e., geometric patterns) that may otherwise have beenunattainable. In some embodiments, an ILT process may be more generallyreferred to as a model-based (MB) mask correction process. To be sure,in some examples, other RET techniques such as those described above andwhich may use a model, for example, to calculate SRAF shapes. etc. mayalso fall within the scope of a MB mask correction process.

The mask data preparation 132 may further include a mask rule checker(MRC) that checks the IC design layout that has undergone one or moreRET processes (e.g., OPC, ILT, etc.) with a set of mask creation ruleswhich may contain certain geometric and connectivity restrictions toensure sufficient margins, to account for variability in semiconductormanufacturing processes, etc. In some cases, the MRC modifies the ICdesign layout to compensate for limitations which may be encounteredduring mask fabrication 144, which may modify part of the modificationsperformed by the one or more RET processes in order to meet maskcreation rules.

In some embodiments, the mask data preparation 132 may further includelithography process checking (LPC) that simulates processing that willbe implemented by the IC manufacturer 150 to fabricate the IC device160. The LPC may simulate this processing based on the IC design layout122 to create a simulated manufactured device, such as the IC device160. The processing parameters in LPC simulation may include parametersassociated with various processes of the IC manufacturing cycle,parameters associated with tools used for manufacturing the IC, and/orother aspects of the manufacturing process. By way of example, LPC maytake into account various factors, such as aerial image contrast, depthof focus (“DOF”), mask error enhancement factor (“MEEF”), other suitablefactors, or combinations thereof. The simulated processing (e.g.,implemented by the LPC) can be used to provide for the generation of aprocess-aware rule table (e.g., for SRAF insertions). Thus, an SRAF ruletable may be generated for the specific IC design layout 122, withconsideration of the processing conditions of the IC manufacturer 150.

In some embodiments, after a simulated manufactured device has beencreated by LPC, if the simulated device layout is not close enough inshape to satisfy design rules, certain steps in the mask datapreparation 132, such as OPC and MRC, may be repeated to refine the ICdesign layout 122 further. In such cases, the previously generated SRAFrule table may also be updated.

It should be understood that the above description of the mask datapreparation 132 has been simplified for the purposes of clarity, anddata preparation may include additional features such as a logicoperation (LOP) to modify the IC design layout according tomanufacturing rules. Additionally, the processes applied to the ICdesign layout 122 during data preparation 132 may be executed in avariety of different orders.

After mask data preparation 132 and during mask fabrication 144, a maskor a group of masks may be fabricated based on the modified IC designlayout. The mask can be formed in various technologies. In anembodiment, the mask is formed using binary technology. In someembodiments, a mask pattern includes opaque regions and transparentregions. A radiation beam, such as an ultraviolet (UV) beam, used toexpose a radiation-sensitive material layer (e.g., photoresist) coatedon a wafer, is blocked by the opaque region and transmitted through thetransparent regions. In one example, a binary mask includes atransparent substrate (e.g., fused quartz) and an opaque material (e.g.,chromium) coated in the opaque regions of the mask. In some examples,the mask is formed using a phase shift technology. In a phase shift mask(PSM), various features in the pattern formed on the mask are configuredto have a pre-configured phase difference to enhance image resolutionand imaging quality. In various examples, the phase shift mask can be anattenuated PSM or alternating PSM.

In some embodiments, the IC manufacturer 150, such as a semiconductorfoundry, uses the mask (or masks) fabricated by the mask house 130 totransfer one or more mask patterns onto a production wafer 152 and thusfabricate the IC device 160 on the production wafer 152. The ICmanufacturer 150 may include an IC fabrication facility that may includea myriad of manufacturing facilities for the fabrication of a variety ofdifferent IC products. For example, the IC manufacturer 150 may includea first manufacturing facility for front end fabrication of a pluralityof IC products (i.e., front-end-of-line (FEOL) fabrication), while asecond manufacturing facility may provide back end fabrication for theinterconnection and packaging of the IC products (i.e., back-end-of-line(BEOL) fabrication), and a third manufacturing facility may provideother services for the foundry business.

In various embodiments, the semiconductor wafer (i.e., the productionwafer 152) within and/or upon which the IC device 160 is fabricated mayinclude a silicon substrate or other substrate having material layersformed thereon. Other substrate materials may include another suitableelementary semiconductor, such as diamond or germanium; a suitablecompound semiconductor, such as silicon carbide, indium arsenide, orindium phosphide; or a suitable alloy semiconductor, such as silicongermanium carbide, gallium arsenic phosphide, or gallium indiumphosphide. In some embodiments, the semiconductor wafer may furtherinclude various doped regions, dielectric features, and multilevelinterconnects (formed at subsequent manufacturing steps). Moreover, themask (or masks) may be used in a variety of processes. For example, themask (or masks) may be used in an ion implantation process to formvarious doped regions in the semiconductor wafer, in an etching processto form various etching regions in the semiconductor wafer, and/or inother suitable processes.

It is understood that the IC manufacturer 150 may use the mask (ormasks) fabricated by the mask house 130 to transfer one or more maskpatterns onto a research and development (R&D) wafer 154. One or morephotolithography processes may be performed on the R&D wafer 154. Afterphotolithography processing of the R&D wafer 154, the R&D wafer 154 maythen be transferred to a test lab (e.g., metrology lab or parametrictest lab) for empirical analysis 156. Empirical data from the R&D wafer154 may be collected and then transferred to the mask house 130 tofacilitate the data preparation 132.

FIG. 2 is a more detailed block diagram of the mask house 130 shown inFIG. 1 according to various aspects of the present disclosure. In theillustrated embodiment, the mask house 130 includes a mask design system180 that is operable to perform the functionality described inassociation with mask data preparation 132 of FIG. 1. The mask designsystem 180 is an information handling system such as a computer, server,workstation, or other suitable device. The system 180 includes aprocessor 182 that is communicatively coupled to a system memory 184, amass storage device 186, and a communication module 188. The systemmemory 184 provides the processor 182 with non-transitory,computer-readable storage to facilitate execution of computerinstructions by the processor. Examples of system memory may includerandom access memory (RAM) devices such as dynamic RAM (DRAM),synchronous DRAM (SDRAM), solid state memory devices, and/or a varietyof other memory devices known in the art. Computer programs,instructions, and data are stored on the mass storage device 186.Examples of mass storage devices may include hard discs, optical disks,magneto-optical discs, solid-state storage devices, and/or a varietyother mass storage devices. The communication module 188 is operable tocommunicate information such as IC design layout files with the othercomponents in the IC manufacturing system 100, such as design house 120.Examples of communication modules may include Ethernet cards, 802.11WiFi devices, cellular data radios, and/or other suitable devices.

In operation, the mask design system 180 is configured to manipulate theIC design layout 122 according to a variety of design rules andlimitations before it is transferred to a mask 190 by mask fabrication144. For example, in an embodiment, mask data preparation 132, includingOPC, ILT, MRC, and/or LPC, may be implemented as software instructionsexecuting on the mask design system 180. In such an embodiment, the maskdesign system 180 receives a first GDSII file 192 containing the ICdesign layout 122 from the design house 120. After the mask datapreparation 132 is complete, the mask design system 180 transmits asecond GDSII file 194 containing a modified IC design layout to maskfabrication 144. In alternative embodiments, the IC design layout may betransmitted between the components in IC manufacturing system 100 inalternate file formats such as DFII, CIF, OASIS, or any other suitablefile type. Further, the mask design system 180 and the mask house 130may include additional and/or different components in alternativeembodiments.

In lithography, the near field of a binary mask pattern resembles themask pattern but has blurred pattern edge. Therefore, it can beapproximated by the thin mask model that assigns two different constantfield values to areas occupied or not occupied by patterns respectively.To improve the accuracy of the near field model, a correction unit—alsoreferred to as a kernel—needs to be determined. Once determined, thekernel is applied along the (sharp) edge of the mask pattern to generatea correction field that will be added to the thin mask field. This willgenerate a field with a blurred edge that closely resembles the truenear field of the mask.

FIG. 3 is a graphical illustration of how a near field of a mask isgenerated using the above process (i.e., by applying akernel-containing-correction-field to a thin mask field). For example,the true near field 200 of a polygonal mask pattern is shown in FIG. 3.As can be seen in FIG. 3, the true near field 200 has blurred edges. Thetrue near field 200 can be approximated by combining a thin mask field210 with a correction field 220. The thin mask field 210 has sharp edges(i.e., not blurry). The correction field 220 includes kernels 230, someexamples of which are illustrated in a magnified window 240 in FIG. 3.An accurate kernel is indispensable for the accurate simulation of thetrue near field of any mask pattern.

Note that the kernel 230 in FIG. 3 is a one-dimensional kernel that onlyvaries along one dimension and is uniform along the other dimension. Aone-dimensional kernel works fine for Manhattan patterns such as thepattern shown in FIG. 3. However, for non-Manhattan patterns, forexample curved patterns or patterns with arbitrary angles that are usedin ILT, the one-dimensional kernels may be insufficient to generate anaccurate correction field, and as such it may be difficult to use theone-dimensional kernels to generate an accurate near field. To overcomethis problem, the present disclosure uses two-dimensional kernels thatcan be quickly rotated. These two-dimensional kernels are used togenerate the correction field, which is then applied to the thin maskfield to generate an accurate near field for the non-Manhattan patternsused in ILT, as discussed below in more detail.

FIG. 4 is a flowchart of a method 300 that illustrates an overall flowof an embodiment of the present disclosure.

The method 300 includes a step 310, in which a mask layout is loaded.The mask layout may be for an ILT mask, which as discussed above maycontain non-Manhattan shapes that are optimized for certain IC patterns.For example, the mask layout loaded herein may include curvilinearpattern edges.

The method 300 includes a step 320, in which the mask layout loaded instep 310 undergoes pre-processing. In some embodiments, thepre-processing may include steps such as rasterization and/oranti-aliasing filtering. Rasterization refers to the task of taking animage described in a vector graphics format (e.g., including thepolygonal shapes of the mask patterns) and converting it into a rasterimage that comprises pixels or dots. In this process, a high resolutionresult may be obtained. However, such a high resolution may not beneeded, and thus the high resolution may be down-converted to a lowerresolution. This down-conversion process may involve signal processingthat could result in aliasing. For high frequency aliasing componentsthat are not of interest, they may be filtered out by the anti-aliasingfiltering step.

The method 300 includes a step 330, in which an edge distribution andorientation maps of the non-Manhattan patterns are built for the masklayout that is processed in step 320. The details of step 330 will bediscussed in greater detail below.

The method 300 includes a step 340, in which different rotationallydecomposed kernels (e.g., two-dimensional kernels) are applied to theedge and orientation maps to get edge correction (for the non-Manhattanpatterns). In other words, the step 340 obtains the correction fieldsimilar to the correction field 220 shown in FIG. 3, though thecorrection field herein uses two-dimensional kernels. The details ofstep 340 will also be discussed in greater detail below.

The method 300 includes a step 350, in which a thin mask model isapplied to the processed mask layout obtained in step 320. As discussedabove, the thin mask model contains binary modeling of the patterns onthe mask. In other words, the thin mask model describes the maskpatterns as having sharp edges (e.g., black and white). When the thinmask model is applied to the processed mask layout, a thin mask field(e.g., the thin mask field 210 in FIG. 3) may be obtained as a result.Of course, since the present disclosure may use non-Manhattan patternson the mask, the thin mask field obtained herein may also havenon-Manhattan shapes.

The method 300 includes a step 360, in which the thin mask result(obtained in step 350) and the edge correction (obtained in steps 340)are combined to obtain a near field. Again, the edge correction may beviewed as the correction field similar to the correction field in FIG. 3(though with two-dimensional kernels). The kernels of the correctionfield may be applied along the edge of the mask pattern to generate thecorrection field that adds a blurred edge to the thin mask field toapproximate the true near field of the mask patterns.

The method 300 includes a step 370, in which an optical model is appliedto the near field (obtained in step 360) to obtain an aerial image onthe wafer. The step 370 may also be viewed as performing an exposuresimulation.

The method 300 includes a step 380, in which a photoresist model isapplied to the aerial image to obtain a final photoresist image on thewafer. The step 380 may also be viewed as performing a photoresistsimulation.

The steps 330 and 340 are now discussed in more detail with reference toFIG. 5, which is a graphical illustration of an example non-Manhattanpattern 400 and a plurality of example two-dimensional kernels 411-416for the non-Manhattan pattern 400. The non-Manhattan pattern 400 isdisplayed in a grid of pixels, where each pixel has an X-axis dimensionΔx and a Y-axis dimension Δy. In some embodiments. Δx and Δy are each ina range from 1 nanometer (nm) to 32 nm. The non-Manhattan pattern 400contains curvilinear edges. The non-Manhattan pattern 400 may also besaid to have arbitrary angles (rather than angles of 0, 90, 180, and 270degrees, as would have been the case with Manhattan patterns). It isunderstood that since the pattern 400 does not have distinctly separateedge segments, it may be considered to have a single continuous edge aswell, where the edge is composed of a plurality of points that each havea two-dimensional kernel associated therewith.

The pixels on which the edge(s) of the non-Manhattan pattern 400 islocated are referred to as edge pixels. A gradient (or a gradientmagnitude) of the pattern may be taken in order to identify these edgepixels. Depending on the gradient method and the anti-aliasing filterapplied, the edges may be several-pixel wide. The edge pixels aredisplayed in FIG. 5 with visual emphasis. Each of these edge pixelscontains a segment of the edge of the non-Manhattan pattern 400. Theorientation of the segment of the edge in each pixel may be determinedby taking the normal line (also referred to as the normal vector) ofthat edge segment. A normal line/vector to a surface refers to aline/vector that is perpendicular or orthogonal to that surface. Thus,the normal line/vector associated with any edge pixel is the line/vectorthat is perpendicular or orthogonal to the segment of the edge in thatparticular pixel.

After the edge pixels have been identified (e.g., by taking thegradient), and the orientation of the edge segment in each pixel hasbeen determined (e.g., by determining the normal line/vector), atwo-dimension kernel is applied to the respective edge segment in eachpixel. The two dimensional kernels may each have their own orientationangle, which is the orientation of the edge segment of the correspondingpixel. In other words, the two-dimensional kernels are rotateddifferently along the edge of the non-Manhattan pattern 400, each as afunction of the orientation of the corresponding edge of thenon-Manhattan pattern 400.

FIG. 5 illustrates two-dimensional kernels 411-416 as examples of theabove concept. For example, the two-dimensional kernel 411 has a firstorientation angle, the two-dimensional kernel 412 has a secondorientation angle, the two-dimensional kernel 413 has a thirdorientation angle, the two-dimensional kernel 414 has a fourthorientation angle, the two-dimensional kernel 415 has a fifthorientation angle, and the two-dimensional kernel 416 has a sixthorientation angle. The first, second, third, fourth, fifth, and sixthorientation angles are all different from one another.

One of the novel aspects of the present disclosure involves a method toquickly and accurately determine the various rotated two-dimensionalkernels that should be applied around the edge of the non-Manhattanpattern 400. This method is graphically illustrated in FIG. 6, whichillustrates the decomposition and rotation of the two-dimensionalkernels. First, an example two-dimensional kernel 450 is provided. Thetwo-dimensional kernel 450 has not been rotated yet, in other words, ithas a 0 degree rotation. Since the kernel 450 is two-dimensional, it hastwo degrees of freedom, which in this case can be expressed using polarcoordinates. For example, the two-dimensional kernel 450's polarcoordinates can be expressed as f_(2D)(r, θ), where the “2D” signifiesthat it is two-dimensional in nature, the “r” represents the radius part(also referred to as the radial coordinate) of the polar coordinates,and the “8” represents the angle part (also referred to as the angularcoordinate or pole angle) of the polar coordinates.

As is shown in FIG. 6, the two-dimensional kernel 450 in this embodimentincludes a portion 450A and a portion 450B that is larger than theportion 450A. The portions 450A and 450B are joined together at a pointthat also corresponds to the origin (i.e., r=0) of the polar coordinatesystem. In FIG. 5, the two-dimensional kernel intersects with each edgepixel at the kernel origin.

The two-dimensional kernel 450 is decomposed into a plurality ofcomponents, some examples of which are shown in FIG. 6 as decomposedcomponents 451, 452, and 453. The decomposed components with differentrotational symmetry are expressed in the form of h_(n)(r)e^(inθ), where“n” is the sequential number of the decomposed component. Thus, “n” is 0for the decomposed component 451, “n” is 1 for the decomposed component452, and “n” is 2 for the decomposed component 453. It is understoodthat “n” covers all integers (positive, negative and 0) and can varyfrom −∞ to ∞. “r” and “θ” are the radial and angular coordinates,respectively. “i” is the square root of negative 1.

It is understood that theoretically, the two-dimensional kernel 450 maybe decomposed into an infinite number of components. The greater thenumber of decomposed components, the more accurate the decomposedcomponents will be able to approximate the two-dimensional kernel 450.In reality, however, a few decomposed components is typically enough toprovide a sufficiently accurate representation of the two-dimensionalkernel 450.

As the two-dimensional kernel 450 is rotated into a two-dimensionalkernel 460, which can be decomposed into a plurality of components, someexamples of which are shown in FIG. 6 as decomposed components 461, 462,and 463. Again, the two-dimensional kernel 460 may be expressed as aninfinite number of decomposed components, but a few decomposedcomponents may be sufficient to approximate the two-dimensional kernel460 accurately. The decomposed components 461-463 are related to (or arefunctions of) the decomposed components 451-453, respectively. Forexample, the decomposed component 461 is the product of the decomposedcomponent 451 and a constant C0, the decomposed component 462 is theproduct of the decomposed component 452 and a constant C1, and thedecomposed component 463 is the product of the decomposed component 453and a constant C2. In the embodiment shown in FIG. 6. C0=1, C1=exp(−iφ),C2=exp (−i2φ), where “exp(x)” refers to the natural exponentialfunction, i.e., same as e^(x). In embodiments where the number ofdecomposed components is n, then the constant Cn may be expressed asexp(−inφ), where “n” is the sequential number of the decomposedcomponent. As discussed above, “n” covers all integers and can vary from−∞ to ∞.

Note that θ and φ represent different things. As discussed above, θrepresents the angular coordinate of the two-dimensional kernel, whichdepends on the location of the two-dimensional kernel in FIG. 5, whereasφ represents the rotation angle (i.e., the orientation angle determinedby taking the normal line/vector of each edge pixel) of thetwo-dimensional kernel in FIG. 5.

It can be seen that since the decomposed components 461-463 can bederived from the decomposed components 451-453 merely by multiplying thedecomposed components 451-453 with their respective constants C0, C1,and C2, the rotation of the two-dimensional kernel 450 (into the rotatedtwo-dimensional kernel 460) can be performed more quickly and moreaccurately than the conventional rotation that transforms the coordinatefrom (x, y) to (x cos φ+y sin φ, y cos φ−x sin φ).

FIG. 7 is a graphical illustration of how to use two-dimensional kernelsto perform an edge correction process for the non-Manhattan mask pattern400 according to an example of the present disclosure. The first step ofthis process is to decompose the two-dimensional kernel 450. Thisdecomposition process is similar to the one discussed above withreference to FIG. 6. However, rather than decomposing thetwo-dimensional kernel 450 into three components, the embodiment shownin FIG. 7 decomposes the two-dimensional kernel 450 into two components451 and 452, where the component 451 is expressed as h₀(r), and thecomponent 452 is expressed as h₁(r)e^(iθ). Of course, it is understoodthat the two components 451 and 452 are just an example, and thetwo-dimensional kernel 450 may be decomposed into any other number ofcomponents in alternative embodiments.

The second step of this process shown in FIG. 7 is to obtain thegradient and the orientation map. The gradient of the pattern 400 isobtained as a magnitude and expressed as |grad(x,y)|. The edge pixelsmay be identified based on the gradient. As discussed above, theorientation map refers to the angle associated with the normalline/vector for each edge pixel. In other words, for each of the edgepixels, the normal line/vector has a corresponding angle or orientation,and the angle/orientation for all the edge pixels collectively may beconsidered an orientation map. For the sake of simplicity, theorientation map is mathematically expressed herein as φ(x,y). Note thatφ(x,y) and φ may be used interchangeably throughout the presentdisclosure, where φ may be a shorthand notation of φ(x,y).

The third step of this process shown in FIG. 7 is to perform the edgecorrection process. As a part of the edge correction process, thegradient magnitude |grad(x,y)| is convolved with the decomposedcomponent 451, and the gradient magnitude |grad(x,y)| is also multipliedwith exp[−iφ(x,y)] (in other words, multiplied with the constant C1discussed above with reference to FIG. 6), and then convolved with thedecomposed component 451.

The results of the two convolutions are then added together to obtainthe edge correction result. The result of the edge correction processrepresents the correction field (e.g., similar to the correction field220 shown in FIG. 3, except with two-dimensional kernels rather thanone-dimensional kernels) for the non-Manhattan pattern 400. Once thecorrection field is obtained, the near field (e.g., similar to the truenear field 200 shown in FIG. 3, except with a non-Manhattan pattern) ofthe pattern 400 may be determined by applying the correction field tothe thin mask field (e.g., similar to the thin mask field 210 in FIG.3).

FIG. 8 is a flowchart illustrating a method 600 of preparing thetwo-dimensional kernels discussed herein. The method 600 includes a step610, in which calibration mask layout pattern samples are generated. Insome embodiments, there may be hundreds of calibration mask layoutpatterns.

The method 600 includes a step 620, in which the mask layout undergoespreprocessing, for example rasterization and anti-aliasing filtering.

The method 600 includes a step 630, in which the thin mask model isapplied to each of the mask patterns processed in step 620.

The method 600 includes a step 640, in which the rigorous near field ofeach processed mask layout is computed. This may be a computationallyintensive process and as such may not be suitable in an actualproduction environment. However, since the method 600 is directed to acalibration environment, the fact that step 640 is computationallyintensive is acceptable.

The method 600 includes a step 650, in which the differences between therigorous near fields (i.e., the results from step 640) and the thin masknear fields (i.e., the results from step 630) are computed. Step 650yields the target correction fields.

The method 600 includes a step 660, in which the edge distribution andorientation maps are built for each of the processed calibration masklayout patterns. In other words, the processes discussed above withreference to FIG. 5 are repeated herein for each of the calibrationpatterns.

The method 600 includes a step 670, in which the near field differenceagainst the maps undergoes regression analysis to get the kernels. As apart of the regression analysis, a plurality of coefficients may besolved. The step 670 may produce a library that can be re-used later togenerate the two-dimensional kernels. These two-dimensional kernels canbe used for different masks too.

FIG. 9 illustrates a simplified example of how two-dimensional kernelsare generated according to the regression analysis discussed in step 670above. In FIG. 9, the term “Δfield” represents the results of step 650of FIG. 8. A Fast Fourier Transform (FFT) is performed to the pattern400, the product of the pattern 400 and the exponential term 401, andthe components 451-452, as shown in FIG. 9. The result is the followingequation:N ₀(k)H ₀(k)+N ₁(k)H ₁(k)=ΔF(k)where k is the two-dimensional index in the FFT space (k=k₁, k₂, . . . ,k_(v)).

If M different samples are generated in step 610, performing FFT onevery sample will give M equations. Knowing ΔF(k) from step 650, thefollowing M linear equations are then used to solve for H₀(k_(i)) andH₁(k_(i)) by the least square method:

N₀₁(k_(i))H₀(k_(i)) + N₁₁(k_(i))H₁(k_(i)) = Δ F₁(k_(i))N₀₂(k_(i))H₀(k_(i)) + N₁₂(k_(i))H₁(k_(i)) = Δ F₂(k_(i)) ⋮N_(0M)(k_(i))H₀(k_(i)) + N_(1M)(k_(i))H₁(k_(i)) = Δ F_(M)(k_(i))The process above will generate a library of two-dimensional kernelsincluding H₀ and H₁ at every interested k_(i) that can be reused formany different mask patterns.

FIG. 10 illustrates the non-Manhattan mask pattern 400 and an aerialimage 700 projected by the pattern 400 on a wafer. The aerial image 700may be viewed as an example of the result of the step 370 of FIG. 4,i.e., by applying an optical model to the near field. Based on FIG. 10,it can be seen that the aerial image 700 closely resembles the originalnon-Manhattan mask pattern 400, meaning that the methods disclosedherein can achieve sufficient accuracy. For example, because thetwo-dimensional kernels can have any arbitrary angle/orientation, theaerial image 700 generated by the present disclosure does not haveunwanted corners or other spurious features that are associated withother methods. In addition, the present disclosure has a time complexityof O(N² lg N) in the “Big O notation” with the fast rotation method,whereas the conventional methods of direct coordinate rotation may havea time complexity of O(N⁴), which is too slow to be applied in OPC orILT computation. Here “N” refers to the size of one side of thetwo-dimensional simulation clip. Based on the difference between O(N² lgN) and O(N⁴), it can be seen that the methods of the present disclosurecan be performed much more quickly in rotating a two-dimensional kernelthat will provide much better flexibility and accuracy compared to theone-dimensional kernels employed by the conventional methods.

FIG. 11 is a flowchart illustrating a method 800 of modeling a mask. Themethod 800 includes a step 810 of receiving a mask layout, the masklayout containing a non-Manhattan pattern.

The method 800 includes a step 820 of processing the mask layout. Insome embodiments, the step 820 involves performing rasterization oranti-aliasing filtering to the mask layout.

The method 800 includes a step 830 of identifying an edge of thenon-Manhattan pattern and the orientation of the edge. In someembodiments, the edge may be identified by taking a gradient of theprocessed mask layout.

The method 800 includes a step 840 of checking whether the decomposedtwo-dimensional kernels have been generated. If not, the decomposedtwo-dimensional kernels will be generated by step 845 that calls method600. The decomposed two-dimensional kernels each have a respectiverotational symmetry. In some embodiments, the step 845 involvesdecomposing each of the two-dimensional kernels into a plurality ofcomponents.

The method 800 includes a step 850 of loading and applying thetwo-dimensional kernels to all the edges of the non-Manhattan pattern toobtain a correction field for the non-Manhattan pattern.

The method 800 includes a step 860 of applying a thin mask model to thenon-Manhattan pattern. The thin mask model contains a binary modeling ofthe non-Manhattan pattern.

The method 800 includes a step 870 of determining a near field of thenon-Manhattan pattern by applying the correction field to thenon-Manhattan pattern having the thin mask model applied thereon.

The method 800 includes a step 880 of applying an optical model to thenear field to obtain an aerial image on a wafer.

The method 800 includes a step 890 of applying a resist model to theaerial image to obtain a final resist image on the wafer.

It is understood that although the method 800 is performed to a masklayout having a non-Manhattan pattern as an example, the method 800 maybe applied to mask layouts having Manhattan patterns too. In addition,additional steps may be performed before, during, or after the steps810-890 herein. For example, the additional steps may includemanufacturing a mask, and/or performing semiconductor fabrication usingthe mask. For reasons of simplicity, these additional steps are notdiscussed in detail herein.

Another aspect of the present disclosure relates to improving theaccuracy of mask models by fully taking edge interactions into account.FIG. 12 is a graphical illustration of an edge interaction between twoadjacent mask patterns 900 and 901. The patterns 900-901 are locatedclose to each other, such that their respective edges 910-911 interactwith each other, which may distort the true near field created by theedges 910-911. In other words, the true near field pattern created by astandalone edge is not the same as the true near field pattern createdby that same edge if another edge is located sufficiently close to it.As is shown in FIG. 12, a true near field 920 created by the twoclosely-located edges 910-911 may include contributions from a kernel930, a kernel 940, as well as contributions from an edge interaction950.

As semiconductor device sizes continue to shrink, the spacing betweenadjacent patterns shrinks too. Whereas edge interactions may not havebeen a problem in older technology generations having larger devicepatterns and spacing, the small feature sizes and tight spacing in thenewer technology generations may enhance the effects of edgeinteractions. Unfortunately, due to the many different possibilities ofhow any two (or more) patterns are located adjacently to one another,conventional methods cannot adequately and accurately account for theedge interaction effects. This is even more true with non-Manhattanpatterns (e.g., the pattern 400 discussed above), since theirirregularly-shaped edges may present many more different possibilitiesof how edges are interacting with one another, and as such thenon-Manhattan patterns may further complicate the calculations of edgeinteraction.

The present disclosure involves a method to accurately and quicklydetermine the edge interaction (and to account for it) for any masklayout, including layouts having non-Manhattan patterns. The improvedaccuracy will help optimize the process window and improve yield. Thevarious aspects of determining the edge interaction is discussed in moredetail below with reference to FIGS. 13-21.

FIG. 13 is a flowchart of a method 1000 that illustrates an overall flowof an embodiment of the present disclosure.

The method 1000 includes a step 1010, in which a mask layout is loaded.The mask layout may be for an ILT mask, which as discussed above maycontain mask patterns having non-Manhattan geometries. For example, themask layout loaded herein may include mask patterns having curvilinearpattern edges.

The method 1000 includes a step 1020, in which the mask layout loaded instep 1010 undergoes pre-processing. In some embodiments, thepre-processing may include steps such as rasterization and/oranti-aliasing filtering discussed above with reference to the step 320in FIG. 4.

The method 1000 includes a step 1030, in which an interaction-free maskmodel is applied to the mask layout processed from step 1020. Theinteraction-free mask model may refer to mask models that do not yethave the edge interaction taken into account. In some embodiments, theinteraction-free mask model is obtained by using the two-dimensionalkernels discussed above with reference to FIGS. 3-11.

The method 1000 includes a step 1040, in which an edge interaction modelaccording to the present disclosure is applied to the mask layoutprocessed from step 1020. The details of step 1040 will also bediscussed in greater detail below.

The method 1000 includes a step 1050, in which a thin mask model isapplied to the mask layout processed from step 1020. In embodimentswhere the step 1030 has obtained the interaction-free mask model byusing the two-dimensional kernels discussed above with reference toFIGS. 3-11, the step 1050 may be omitted herein, because it would havealready been performed as a part of the step 1030.

The method 1000 includes a step 1060, in which the results from steps1030, 1040, and 1050 are all combined to obtain a near field for themask layout.

The method 1000 includes a step 1070, in which an optical model isapplied to the near field (obtained in step 1060) to obtain an aerialimage of the mask layout on a wafer. The step 1070 may also be viewed asperforming an exposure simulation.

The method 1000 includes a step 1080, in which a photoresist model isapplied to the aerial image to obtain a final photoresist image of themask layout on the wafer. The step 1080 may also be viewed as performinga photoresist simulation.

Referring now to FIG. 14, a flowchart of a method 1100 of performing thestep 1040 of FIG. 13 is illustrated. The method 1100 includes a step1110, in which the edge and orientation maps of the processed masklayout are built. Again, this step 1110 may apply the same method thatis employed by the two-dimensional kernels discussed above withreference to FIGS. 3-11, so that non-Manhattan patterns with arbitraryangles can be accurately modeled.

The method 1100 includes a step 1120, in which a whole simulation domain(e.g., a mask layout where the edge interaction effect needs to bedetermined) is divided into small tiles of moderate sizes. For example,a side of the tile may have a dimension in a range from 20 nm to 100 nm.The reason for the small tiles is because the edge interaction will comeinto play at small distances, which can be accounted for within a smalltile. Therefore, larger tiles are not needed to account for the edgeinteraction. Note that if an edge crosses over two tiles (i.e., eachtile contains a segment of the edge), then that edge may be calculatedtwice in some embodiments.

The method 1100 includes a step 1130, in which a two-edge (2E)interaction model is applied for each of the small tiles generated instep 1120 to get the two-edge correction results. In other words, withineach of the small tiles, the various possible pairs of edges areidentified, and the edge interaction between each possible pair of edgesis calculated.

The method 1100 includes a step 1140, in which the two-edge interactionresults from every small tile are combined to determine the totaltwo-edge interaction correction results for the pattern as a whole.

The method 1100 includes a step 1150, in which a three-edge (3E)interaction model is applied for each of the small tiles generated instep 1120 to get the three-edge correction results. In other words, thestep 1150 is similar to step 1130, except that it is performed withvarious combinations of three edges rather than two edges.

The method 1100 includes a step 1160, in which the three-edgeinteraction results from every small tile are combined to determine thetotal three-edge interaction correction results for the pattern as awhole. In other words, the step 1160 is similar to step 1140, exceptthat it is performed with various combinations of three edges ratherthan two edges.

The method 1100 includes a step 1170, in which the total two-edgeinteraction correction results from step 1140 and the total three-edgeinteraction correction results from step 1160 are combined to determinethe total edge interaction correction results. It is understood that intheory, steps similar to steps 1130-1140 may be repeated for the casesof four-edge interactions, five-edge interactions, and so on. Inreality, however, two-edge and three-edge interactions may be sufficientto determine the edge interaction correction with sufficient accuracy.

The steps 1130-1140 are now discussed in more detail with reference toFIG. 15, which is a graphical illustration of how a two-edge (2E) kernelis defined. FIG. 15 illustrates a tile 1200, which is an example of oneof the small tiles obtained by dividing the simulation domain. In otherwords, the tile 1200 represents an example portion of a mask layout thatneeds to be modeled to take into account of the edge interaction effectdiscussed above. The tile 1200 is displayed as a grid of pixels, whereeach pixel has an X-axis dimension Δx and a Y-axis dimension Δy. In someembodiments. Δx and Δy are each in a range from 1 nanometer (nm) to 32nm.

The tile 1200 includes a non-Manhattan pattern 1210 and a non-Manhattanpattern 1211. Similar to the non-Manhattan pattern 400 discussed above,the non-Manhattan patterns 1210-1211 each include curvilinear edges. Ofcourse, these patterns 1210-1211 shown herein are merely examples, andthat other patterns such as Manhattan patterns may be included in thetile in other embodiments. In order to determine the edge interactionmodel in step 1040 discussed above, the patterns 1210-1211 areconsidered in terms of pixels rather than geometry. For example, for anygiven pixel (not necessarily an edge pixel), such as pixel r, it isinfluenced by the edge interaction from any two edge pixels, such aspixels r₁ and r₂, that are each located on an edge of one of thepatterns 1210-1211. The pixels r₁ and r₂ may also be referred to asinteracting edge pixels, and the pixel r may also be referred to as aninfluenced pixel. Of course, the pixel r may experience edge interactioninfluences from any other possible combination of two edge pixels (notjust r₁ and r₂), and r₁ and r₂ may also influence other pixels (not justr). In some embodiments, the pixels r₁ and r₂ are located within apredefined proximity or distance of each other, for example within Nnanometers, where N may be in a range from about 1 nm to about 100 nm.As discussed above with reference to FIG. 5, the edge pixels may bedetermined by taking the gradient. The edge pixels r₁ and r₂ also haveorientation angles φ₁ and φ₂, respectively, which as discussed above maybe obtained by taken the normal line or normal vector at the edgesegment in the pixel. The normal lines for the pixel r₁ and r₂ have beengraphically illustrated in FIG. 15 as arrows with dotted lines pointingaway from the edges.

Based on the influence exerted to the pixel r by the pair of edge pixelsr_(j) and r₂, a two-edge interaction kernel G₂ is defined. The kernel G₂describes the near field correction at the pixel r due to theinteraction between the two edge pixels edge pixels r₁ and r₂. Thekernel G₂ may be expressed as G₂(r, r₁, r₂, φ₁, φ₂), in other words, thekernel G₂ is a function of r, r₁, r₂, φ₁, φ₂. It is understood that r,r₁, r₂ are two-dimensional position vectors herein. For example, r, r₁,and r₂ may each be represented in a polar coordinate system and as suchmay include a radial coordinate and angular coordinate. The radial andangular coordinates are determined based on the location of theirrespective pixels relative to the origin of the simulated tile.

Thus, for any given influenced pixel (such as the pixel r), a respectivetwo-edge kernel may be determined for any possible pair of twointeracting edges (such as the edges located in pixels r₁ and r₂). Inthe end, an integral or a summation is taken for all these two-edgekernels to obtain the true near field correction at the influenced pixelr. This process may also be repeated for each pixel in the tile 1200.This will yield the two-edge correction field (based on the interactionof two-edges) as the result of step 1140 of FIG. 14 discussed above.

The steps 1150-1160 are now discussed in more detail with reference toFIG. 16, which is a graphical illustration of how a three-edge kernel isdetermined. FIG. 16 and FIG. 15 share many similarities. For example,they both illustrate a tile 1200 in which non-Manhattan patterns 1210and 1211 are included. However. FIG. 16 illustrates how the pixel r isinfluenced by a combination of three edges r₁, r₂, and r₃. Otherwise,the process to determine the edge interaction in FIG. 16 is similar tothat discussed above in association with FIG. 15. Accordingly, athree-edge kernel G₃ can be determined as a function of r, r₁, r₂, r₃,φ₁, φ₂, φ₃. Again, r, r₁, r₂, and r₃ are two-dimensional positionvectors, for example they may be represented in a polar coordinatesystem that each have a radial coordinate and an angular coordinate,depending on the locations of their respective pixels relative to theorigin of the simulated tile. The orientation angles φ₁, φ₂, and φ₃ aredetermined by taking the normal lines of the edge in the respectivepixels. As is the case for the two-edge kernel G₂ in FIG. 15, thethree-edge kernel G₃ in FIG. 16 can be integrated or summed up withrespect to all possible combinations of three edges, and for eachinfluenced pixel. This will yield the three-edge correction model forstep 1160.

With the results of both the two-edge correction model and thethree-edge correction model, they may be combined to generate the edgecorrection field for the tile 1200. Again, theoretically the aboveprocess may be repeated for a four-edge correction model, five-edgecorrection model, etc., but that may be reaching a point of diminishingreturns, since a two-edge correction model and a three-edge correctionmodel may be sufficient to approximate the overall edge correction modelaccurately.

FIG. 17 illustrates two techniques for accelerating the kernelcomputations discussed above. The first technique is dividing thesimulation domain into smaller tiles to perform the kernel computations.A simulation domain 1250 is illustrated in FIG. 17. The simulationdomain 1250 may include one or more mask patterns (which may benon-Manhattan patterns) for which the edge interaction needs to bedetermined. The simulation domain 1250 in the illustrated embodimentresembles a rectangle and includes a first dimension of size N1 and asecond dimension of size N2. In some embodiments, N1 and N2 are each ina range between 4 microns and 16 microns.

If the two-edge kernel or three-edge kernel computations discussed aboveare performed on the simulation domain 1250, it may take too long due tothe relatively large size of the simulation domain. Thus, as discussedabove in FIGS. 15-16, the simulation domain 1250 is divided into aplurality of smaller tiles in order to speed up the calculations. Someof the tiles are illustrated herein as tiles 1260-1267. Limitingcomputations within the tiles should not affect the final result of thewhole edge interaction field since edges outside of a given tile may betoo far to exert influence on pixels within that tile anyway.

The tiles 1260-1267 have dimensions of M1×M2. In some embodiments. M1and M2 are each in a range between 20 nm and 100 nm. However, during theedge kernel computations, each tile also includes a margin ofinteraction 1300. Without adding the margin of interaction, an implicitassumption is made that the tiles have periodic boundary conditions,which is a false assumption. Accordingly, the kernel computationsperformed without taking the margin of interaction 1300 into accountwould have yield incorrect results. Thus, the present disclosuresurrounds each tile with a respective margin of interaction 1300. Thekernel computations discussed above with reference to FIGS. 15-16 areperformed within the margin of interaction 1300 (including the tile thatis surrounded therein) to ensure that the results are accurate.Thereafter, only the kernel computation results attributed to the tileitself are kept, whereas the kernel computation results attributed tothe margin of interaction (but that are outside of the tile itself) arediscarded. As is shown in FIG. 17, the margin of interaction 1300 has alength L on each side. In some embodiments. L is in a range between 20nm and 100 nm. In some embodiments, M1=M2=L in order to optimize thespeed of calculations.

The second technique for speeding up the computations involvesexploiting the translational and rotational symmetries to decompose theedge-interaction kernels G₂, G₃, etc. For example, the two-edge kernelG₂ may be decomposed according to the following equation:

${G_{2}\left( {r,r_{1},r_{2},\varphi_{1},\varphi_{2}} \right)} = {\sum\limits_{l_{1},l_{2}}^{\;}{e^{{- {il}_{1}}\varphi_{1}}e^{{- {il}_{2}}\varphi_{2}}{G_{2}^{({l_{1}l_{2}})}\left( {{r - r_{1}},{r - r_{2}}} \right)}}}$where l₁ and l₂ represent the index obtained after a Fourier seriesexpansion performed due to a periodicity of the G₂ function (e.g., G₂ isperiodic with respect to φ₁ and φ₂). Technically, l₁ and l₂ each varyfrom −∞ to +∞. Practically though, only a few numbers of l₁ and l₂ areneeded (such as 0, 1, 2, or alternatively −1, 0, and 1) to obtain asufficiently accurate approximation of G₂. Note that due to thetranslational symmetry, only the relative positions between r and r₁(and likewise between r and r₂) matter (as opposed to knowing theabsolute positions for r, r₁, and r₂) for purposes of decomposing thetwo-edge kernel G₂, which helps simplify the computations. Again, the G₂herein describes the correction field for any given influenced pixel rdue to the edge interaction between two edge pixels r₁ and r₂. Thethree-edge kernel G₃ may be obtained in a similar fashion.

FIG. 18 is a graphical illustration of how to use the edge-kernels toperform an edge correction process according to an example of thepresent disclosure. As an example, the two-edge kernel G₂ is usedherein. However, the following discussions apply to the three-edgekernel G₃ as well.

The first step of this process is to compute the edge and orientationmaps of a pattern. The pattern may be a non-Manhattan pattern, such asthe pattern 400 discussed above (or the patterns 1210-1211 discussedabove). The edge (e.g., the edge pixels) of the pattern is computed byobtaining the gradient of the pattern 400, where the gradient mayinclude a magnitude and is expressed as |grad(x,y)|. As discussed above,the orientation map refers to the angle associated with the normalline/vector for each edge pixel. In other words, for each of the edgepixels, the normal line/vector has a corresponding angle or orientation,and the angle/orientation for all the edge pixels collectively may beconsidered an orientation map. For the sake of simplicity, theorientation map is mathematically expressed herein as φ(x,y).

The second step of this process is to compute the mask rotationcomponents Q_(l) for the interested l's. This is mathematicallyexpressed as: Q_(l)(x,y)=|grad(x,y)|× exp[−i l φ(x,y)], where Q_(l)(x,y)represents the mask rotation components. Again, although the term l mayvary from negative infinity to infinity, the practical computationsherein may only select a few interested l's (e.g., 1, 2, 3) to simplifythe computations.

The third step of this process shown in FIG. 18 is to compute thetwo-edge correction. The following equation is used for thiscomputation:

${\Delta\;{m_{2E}(r)}} = {\sum\limits_{l_{1},l_{2}}^{\;}{\int{\int{{Q_{l_{1}}\left( r_{1} \right)}{Q_{l_{2}}\left( r_{2} \right)}{G_{2}^{({l_{1}l_{2}})}\left( {{r - r_{1}},{r - r_{2}}} \right)}{dr}_{1}{dr}_{2}}}}}$where Δm_(2E)(r) represents the two-edge correction, where r, r₁, and r₂are two-dimensional spatial position vectors, and where both l₁ and l₂loop over all interested l's. In other words, Δm_(2E)(r) describes thecorrection field obtained for any given influenced pixel r due to allthe possible combinations of two edge pixels (because of the integralsin Δm_(2E)(r)). As r varies, then the calculated correction fieldΔm_(2E)(r) varies as well, since the correction field Δm_(2E)(r) is afunction of the influenced pixel r. Once Δm_(2E)(r) is calculated forall possible r's, the overall edge correction field can be determined bycombining the results of the correction field associated with all theindividual influenced pixels r.

FIG. 19 is a flowchart illustrating a method 1500 of obtaining thetwo-dimensional kernels discussed herein. The method 1500 includes astep 1510, in which calibration mask layout pattern samples aregenerated. In some embodiments, there may be hundreds of calibrationmask layout patterns.

The method 1500 includes a step 1520, in which the mask layout undergoespreprocessing, for example rasterization and anti-aliasing filtering.

The method 1500 includes a step 1530, in which the thin mask model isapplied to each of the pre-processed mask patterns.

The method 1500 includes a step 1540, in which the edge-interaction-freemodel is applied to each processed mask layout. This step computes theedge correction without considering the edge interaction.

The method 1500 includes a step 1550, in which the rigorous near fieldof each processed mask layout is computed. This may be a computationallyintensive process and as such may not be suitable in an actualproduction environment. However, since the method 1500 is directed to acalibration environment, the fact that step 1550 is computationallyintensive may be irrelevant.

The method 1500 includes a step 1560, in which a difference is computed.The difference is between the results from step 1550 (i.e., the rigorousnear field computations) and the results of steps 1530 and 1540 (i.e.,the thin mask model and the interaction-free mask model). In otherwords, the results of steps 1530 and 1540 are each subtracted from theresults of step 1550, and that will yield the result of step 1560. Theresult of step 1560 is the “residue” left by the edge interaction.

The method 1500 includes a step 1570, in which the edge distribution andorientation maps are built for each of the processed calibration masklayout patterns.

The method 1500 includes a step 1580, in which the near field differenceagainst the maps undergoes regression analysis to get the kernels. As apart of the regression analysis, a plurality of coefficients may besolved. The step 1580 may produce a library that can be re-used later togenerate the two-dimensional kernels. These two-dimensional kernels canbe used for different masks too.

FIG. 20 illustrates some computational details involved in performingthe step 1580 (e.g., the regression analysis) discussed above withreference to FIG. 19. First, the computational results obtained fromstep 1560 discussed above is represented using the following equation:

${\Delta\;{m_{2E}(r)}} = {\sum\limits_{l_{1},l_{2}}^{\;}{\int{\int{{Q_{l_{1}}\left( r_{1} \right)}{Q_{l_{2}}\left( r_{2} \right)}{G_{2}^{({l_{1}l_{2}})}\left( {{r - r_{1}},{r - r_{2}}} \right)}{dr}_{1}{dr}_{2}}}}}$where Q_(l1)(r₁) and Q_(l2)(r₂) are the mask rotation componentsobtained from the computational results of step 1570 discussed above.

A Fast Fourier Transform (FFT) is performed to the above equation toobtain the following equation:

${\Delta\;{{\overset{\sim}{m}}_{2E}(k)}} = {\sum\limits_{l_{1},l_{2}}^{\;}{\sum\limits_{k_{1}}^{\;}{{{\overset{\sim}{Q}}_{l_{1}}\left( k_{1} \right)}{{\overset{\sim}{Q}}_{l_{2}}\left( {k - k_{1}} \right)}{{\overset{\sim}{G}}_{2}^{({l_{1}l_{2}})}\left( {k_{1},{k - k_{1}}} \right)}}}}$

With a small interaction tile, the total number of the grid points ofk's and k₁'s over the two-dimensional frequency space should bemoderate. For example, the number of distinct spatial frequencies is 100on a two-dimensional simulation domain of 50 nm×50 nm with 5-nm gridsize. It is understood that if an M number of layout samples areemployed in step 1510 discussed above, then there will be an M number ofequations for each k. For each pattern, Q_(l) can be computed with theedge and orientation maps computed in step 1570, so there are a numberof linear equation sets to solve for the unknown two-dimensional kernelsG₂'s. With a large enough M, a linear regression method can be appliedto solving for G₂'s at every (k₁, k−k₁) for every l₁ and l₂.

FIG. 21 illustrates a method 1800 of modeling a mask according to anembodiment of the present disclosure. The method 1800 includes a step1810 of receiving a mask layout. The mask layout includes one or morenon-Manhattan patterns.

The method 1800 includes a step 1820 of processing the received masklayout. In some embodiments, the step 1820 may include performingrasterization or anti-aliasing filtering on the mask layout.

The method 1800 includes a step 1830 of applying an interaction-freemask model to the processed mask layout. In some embodiments, theinteraction-free mask model may be obtained by performing the methodsdiscussed above with reference to FIGS. 3-11 using the two-dimensionalkernels.

The method 1800 includes a step 1840 of checking whether the edgeinteraction kernels have been generated. If not, the edge interactionkernels will be generated by step 1845 that calls the method 1500. Thestep 1845 comprises computing a plurality of kernels that each describea correction field at an influenced pixel due to an interaction betweentwo or more edge pixels each located on an edge of the one or morenon-Manhattan patterns. In some embodiments, the computing the pluralityof kernels comprises computing each of the kernels as a function of: alocation of the influenced pixel, a respective location of each of thetwo or more edge pixels, and a respective orientation angle associatedwith each of the two or more edge pixels.

The method 1800 includes a step 1850 of applying the edge interactionmodel to the processed mask layout. In some embodiments, the applyingthe edge interaction model comprises: dividing the mask layout into aplurality of tiles, the tiles each being surrounded by a margin ofinteraction length; computing the edge interaction correction field foreach of the tiles; and determining the total edge interaction correctionfield for the mask layout by combining the edge interaction correctionfield from each tile.

The method 1800 includes a step 1860 of applying a thin mask model tothe mask processed layout.

The method 1800 includes a step 1870 of determining a near field of themask layout based on the applying of the interaction-free mask model,the applying of the edge interaction model, and the applying of the thinmask model.

The method 1800 includes a step 1880 of applying an optical model to thenear field to obtain an aerial image of the mask layout on a wafer.

The method 1800 includes a step 1890 of applying a resist model to theaerial image to obtain a final resist image on the wafer.

It is understood that although the method 1800 is performed to a masklayout having a non-Manhattan pattern as an example, the method 1800 maybe applied to mask layouts having Manhattan patterns too. In addition,additional steps may be performed before, during, or after the steps1810-1890 herein. For example, the additional steps may includemanufacturing a mask, and/or performing semiconductor fabrication usingthe mask. For reasons of simplicity, these additional steps are notdiscussed in detail herein.

One aspect of the present disclosure involves a method. A mask layout isreceived. A set of two-dimensional kernels is generated based on a setof pre-selected mask layout samples. The set of two-dimensional kernelsis applied to the received mask layout to obtain a correction field. Anear field of the received mask layout is determined based at least inpart on the correction field.

Another aspect of the present disclosure involves a method. A masklayout is received. The received mask layout contains a non-Manhattanpattern. A plurality of two-dimensional kernels is generated based on aset of pre-selected mask layout samples. The two-dimensional kernelseach have a respective rotational symmetry. The two-dimensional kernelsare applied to all the edges of the non-Manhattan pattern to obtain acorrection field for the non-Manhattan pattern. A near field of thenon-Manhattan pattern is determined based at least in part on thecorrection field.

Yet another aspect of the present disclosure involves a method. A masklayout that contains a non-Manhattan pattern is received. The receivedmask layout is processed. An edge of the non-Manhattan pattern and theorientation are identified. A plurality of two-dimensional kernels isgenerated based on a set of processed pre-selected mask layout samples.The two-dimensional kernels each have a respective rotational symmetry.The two-dimensional kernels are applied to all the edges of thenon-Manhattan pattern to obtain a correction field for the non-Manhattanpattern. A thin mask model is applied to the non-Manhattan pattern. Thethin mask model contains a binary modeling of the non-Manhattan pattern.A near field of the non-Manhattan pattern is determined by applying thecorrection field to the non-Manhattan pattern having the thin mask modelapplied thereon. An optical model is applied to the near field to obtainan aerial image on a wafer. A resist model is applied to the aerialimage to obtain a final resist image on the wafer.

Another aspect of the present disclosure involves a method. A masklayout is received. An interaction-free mask model is applied to themask layout. An edge interaction model is applied to the mask layout.The edge interaction model describes the influence due to a plurality ofcombinations of two or more edges interacting with one another. A thinmask model is applied to the mask layout. A near field is determinedbased on the applying of the interaction-free mask model, the applyingof the edge interaction model, and the applying of the thin mask model.

Yet another aspect of the present disclosure involves a method. A masklayout is received. The received mask layout includes one or morenon-Manhattan patterns. An interaction-free mask model is applied to thereceived mask layout. An edge interaction model is generated based on aset of pre-selected mask layout samples. The edge interaction modelcomputes the influence exerted to a plurality of pixels of the masklayout by a plurality of combinations of two or more edge segments ofthe one or more non-Manhattan patterns. The edge interaction model isapplied to the received mask layout. A thin mask model is applied to thereceived mask layout. A near field of the received mask layout isdetermined based on the applying of the interaction-free mask model, theapplying of the edge interaction model, and the applying of the thinmask model.

One more aspect of the present disclosure involves a method. A masklayout is received. The received mask layout includes one or morenon-Manhattan patterns. The received mask layout is processed. Aninteraction-free mask model is applied to the processed received masklayout. An edge interaction model is generated based on a set ofpre-selected mask layout samples. The generating comprises computing aplurality of kernels that each describe a correction field at aninfluenced pixel due to an interaction between two or more edge pixelseach located on an edge of the one or more non-Manhattan patterns. Theedge interaction model is applied to the processed received mask layout.A thin mask model is applied to the processed received mask layout. Anear field of the received mask layout is determined based on theapplying of the interaction-free mask model, the applying of the edgeinteraction model, and the applying of the thin mask model. An opticalmodel is applied to the near field to obtain an aerial image of thereceived mask layout on a wafer. A resist model is applied to the aerialimage to obtain a final resist image on the wafer.

The foregoing outlines features of several embodiments so that those ofordinary skill in the art may better understand the aspects of thepresent disclosure. Those of ordinary skill in the art should appreciatethat they may readily use the present disclosure as a basis fordesigning or modifying other processes and structures for carrying outthe same purposes and/or achieving the same advantages of theembodiments introduced herein. Those of ordinary skill in the art shouldalso realize that such equivalent constructions do not depart from thespirit and scope of the present disclosure, and that they may makevarious changes, substitutions, and alterations herein without departingfrom the spirit and scope of the present disclosure.

What is claimed is:
 1. A method, comprising: receiving a mask layoutthat includes one or more non-Manhattan patterns, wherein the one ormore non-Manhattan patterns includes two or more curvilinear edges,wherein the mask layout includes a plurality of pixels, and wherein asubset of the pixels are edge pixels that are located on the two or morecurvilinear edges; applying an interaction-free mask model to the masklayout; applying an edge interaction model to at least the one or morenon-Manhattan patterns of the mask layout, the edge interaction modeldescribing an influence exerted on each of the plurality of pixels dueto a plurality of combinations of the edge pixels of the two or morecurvilinear edges interacting with one another; applying a thin maskmodel to the mask layout; and determining a near field based on theapplying of the interaction-free mask model, the applying of the edgeinteraction model, and the applying of the thin mask model.
 2. Themethod of claim 1, further comprising: identifying the edge pixels bytaking a normal vector of each of a plurality of segments of the two ormore curvilinear edges.
 3. The method of claim 1, wherein the applyingthe edge interaction model comprises: dividing the mask layout into aplurality of tiles; computing an edge interaction correction for each ofthe tiles; and determining a total edge interaction correction for anentirety of the mask layout by combining the edge interaction correctionfrom each of the tiles.
 4. The method of claim 3, wherein: the computingthe edge interaction correction comprises computing a plurality ofkernels; and the kernels each describe a correction field at aninfluenced pixel due to an interaction between two or more of the edgepixels.
 5. The method of claim 4, wherein the computing the plurality ofkernels comprises computing each of the kernels as a function of: alocation of the influenced pixel, a respective location of each of thetwo or more of the edge pixels, and a respective orientation angleassociated with each of the two or more of the edge pixels.
 6. Themethod of claim 3, wherein the dividing comprises: adding a margin ofinteraction length to each of the tiles.
 7. The method of claim 1,wherein the one or more non-Manhattan patterns have angles other than 0degrees, 90 degrees, 180 degrees, or 270 degrees.
 8. The method of claim1, wherein the two or more curvilinear edges interacting with oneanother are located within a predefined proximity to one another.
 9. Themethod of claim 1, further comprising: processing the mask layout,wherein the applying of the interaction-free mask model, the applying ofthe edge interaction model, and the applying of the thin mask model areperformed to the processed mask layout.
 10. The method of claim 9,wherein the processing the mask layout comprises performingrasterization or anti-aliasing filtering to the mask layout.
 11. Themethod of claim 1, wherein the thin mask model contains binary modelingof patterns on the mask layout.
 12. The method of claim 1, furthercomprising: applying an optical model to the near field to obtain anaerial image on a wafer; and applying a resist model to the aerial imageto obtain a final resist image on the wafer.
 13. A method, comprising:receiving a mask layout, the mask layout including one or morenon-Manhattan patterns that each have two or more curvilinear edgesegments, wherein the mask layout includes a plurality of pixels;identifying, from the plurality of pixels, a plurality of edge pixelsthat are located on the two or more curvilinear edge segments, whereinthe identifying comprise taking a normal vector of each of the two ormore curvilinear edge segments; applying an interaction-free mask modelto the received mask layout; generating an edge interaction model with aset of pre-selected mask layout samples, wherein the generatingcomprises determining an influence exerted to each of the plurality ofpixels of the mask layout samples by a plurality of combinations of theedge pixels; applying the edge interaction model to at least the one ormore non-Manhattan patterns of the received mask layout; applying a thinmask model to the received mask layout; and determining a near field ofthe received mask layout based on the applying of the interaction-freemask model, the applying of the edge interaction model, and the applyingof the thin mask model.
 14. The method of claim 13, wherein thegenerating the edge interaction model comprises: dividing the masklayout samples into a plurality of tiles; computing an edge interactionfield for each of the tiles by computing a plurality of kernels, whereinthe kernels each describe a correction field at an influenced pixel dueto an interaction between two or more of the edge pixels; anddetermining one or more edge interaction kernels for a tile.
 15. Themethod of claim 14, wherein the computing the plurality of kernelscomprises computing each of the kernels as a function of: a location ofthe influenced pixel, a respective location of each of the two or moreof the edge pixels, and a respective orientation angle associated witheach of the two or more of the edge pixels.
 16. The method of claim 14,wherein the dividing comprises: adding a margin of interaction length toeach of the tiles.
 17. The method of claim 13, further comprising:processing the received mask layout at least in part by performingrasterization or anti-aliasing filtering to the received mask layout,wherein the applying of the interaction-free mask model, the applying ofthe edge interaction model, and the applying of the thin mask model areperformed to the processed received mask layout; applying an opticalmodel to the near field to obtain an aerial image of the received masklayout on a wafer; and applying a resist model to the aerial image toobtain a final resist image on the wafer.
 18. A method, comprising:receiving a mask layout, the mask layout including one or morenon-Manhattan patterns that each have two or more curvilinear edges,wherein the mask layout includes a plurality of pixels; processing thereceived mask layout, including identifying a plurality of edge pixelsthat are located on the two or more curvilinear edges, wherein theidentifying includes taking a normal vector of each of a plurality ofsegments of the two or more curvilinear edges; applying aninteraction-free mask model to the processed received mask layout;generating an edge interaction model with a set of pre-selected masklayout samples, wherein the generating comprises computing a pluralityof kernels that each describe a correction field at an influenced pixelof the plurality of pixels due to an interaction between a plurality ofdifferent combinations of the edge pixels; applying the edge interactionmodel to the one or more non-Manhattan patterns of the processedreceived mask layout; applying a thin mask model to the processedreceived mask layout; determining a near field of the received masklayout based on the applying of the interaction-free mask model, theapplying of the edge interaction model, and the applying of the thinmask model; applying an optical model to the near field to obtain anaerial image of the received mask layout on a wafer; and applying aresist model to the aerial image to obtain a final resist image on thewafer.
 19. The method of claim 18, wherein the generating the edgeinteraction model comprises: dividing the mask layout samples into aplurality of tiles, the tiles each being surrounded by a margin ofinteraction length; and determining the edge interaction model for atile.
 20. The method of claim 18, wherein the computing the plurality ofkernels comprises computing each of the kernels as a function of: alocation of the influenced pixel, a respective location of each of thedifferent combinations of the edge pixels, and a respective orientationangle associated with each of the different combinations of the edgepixels.